Perry: Your use of axiomatic is one I had never thought of. I suppose I need a wider vision of the word. The root of "axiom" is something like "appropriate" in Greek but does come to us as sort of meaning “obvious”. In mathematics, it is the minimal set of rules from which one may construct a complete mathematical system. They say that if one disallows the axiom of choice then one can never prove the existence of irrational numbers. I have just done a quick reviewed my fifty-five year old mathematics MS experience, and I no longer know what that means, if I ever did. In Point Set Theory class, I tried to point out that the whole thing was irrational, but my professor didn't get the joke. I think I detect a hint of a joke in William's initial comment. Keep on truckin'.

As a philosophy major, I took a course in symbolic or mathematical logic, hoping to find new ways to reason. Instead I found GIGO before computers. Logic makes sure you aren't reasoning irrationally, but doesn't really discover anything new, since you've already included it with the input. Thus I have recently begun drafting a paper on axioms, what they are, and how you choose them. So far I'm stuck on defining words.